1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Korolek [52]
3 years ago
12

fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed w

ith a mean of 700 hours and a standard deviation of 45 hours. Test the hypothesis that mean is 700 hours against the alternat
Mathematics
1 answer:
EastWind [94]3 years ago
6 0

Answer:

The p-value obtained is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours

Step-by-step explanation:

Complete Question

fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed with a mean of 700 hours and a standard deviation of 45 hours. Test the hypothesis that mean is 700 hours against the alternative hypothesis that the mean is not equal to 700 hours, if a random sample of 30 bulbs has an average life of 688 hours. Use a P-value in your answer.

Solution

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the mean life of the fluorescent lights is 700 hours.

The alternative hypothesis will now be that the mean life of the fluorescent lights is significantly different from 700 hours.

Mathematically,

The null hypothesis is represented as

H₀: μ = 700

The alternative hypothesis is represented as

Hₐ: μ ≠ 700

To do this test, we will use the z-distribution because no information on the population standard deviation is known

So, we compute the z-test statistic

z = (x - μ₀)/σₓ

x = sample mean = 688 hours

μ₀ = 700 hours

σₓ = standard error = (σ/√n)

σ = standard deviation = 45 hours

n = Sample size = 30

σₓ = (45/√30) = 8.2158383626 = 8.216

z = (688 - 700) ÷ 8.216

z = 1.46

checking the tables for the p-value of this z-statistic

Significance level = 0.05 (This is used when significance level isn't given)

The hypothesis test uses a two-tailed condition because we're testing in two directions.

p-value (for z = 1.46, at 0.05 significance level, with a two tailed condition) = 0.14429

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.14429

0.14429 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours.

Hope this Helps!!

You might be interested in
This table shows some values of an exponential function. what is the function
Yuri [45]

Answer:

there is no table so we are therefore unable to answer this question

Step-by-step explanation:

sorry

4 0
2 years ago
Wat is the scientific notation for 0.00000012 and 0.000005008
gtnhenbr [62]
Scientific notation is a way of writing numbers in a form of a decimal multiplied by an exponent of 10.
For these, the exponent will be negative, since they're teeny tiny decimals, and we'll have to move the decimal point back to the right.
0.00000012 will become 1.2* 10^{-7}
This is because the decimal point is moved seven places to the right of where it originally was.
0.000005008 will become 50.08* 10^{-7}
Again, this is because the decimal point is moved seven places to the right of where it originally was.
So, your scientific notations are 1.2* 10^{-7} and 50.08* 10^{-7}
6 0
3 years ago
Read 2 more answers
A rectangle has one side that measures 3x + 1 and another that measures 4y + 3. Keith says that the perimeter of the rectangle i
mart [117]

Answer:

he added the dimensions of the rectangle. He used the wrong formula. the formula he used was length + breadth. He should have multiplied by 2

6x + 8y +8

Step-by-step explanation:

Perimeter of a rectangle = 2 x (L + B)

L = length

b = breadth

2 (3x + 4y + 4. ) = 6x + 8y +8

5 0
3 years ago
The average value of a function f over the interval [−2,3] is −6 , and the average value of f over the interval [3,5] is 20. Wha
Xelga [282]

Answer:

The average value of f over the interval [-2,5] is \frac{10}{7}.

Step-by-step explanation:

Let suppose that function f is continuous and integrable in the given intervals, by integral definition of average we have that:

\frac{1}{3-(-2)} \int\limits^{3}_{-2} {f(x)} \, dx = -6 (1)

\frac{1}{5-3} \int\limits^{5}_{3} {f(x)} \, dx = 20 (2)

By Fundamental Theorems of Calculus we expand both expressions:

\frac{F(3)-F(-2)}{3-(-2)} = -6

F(3) - F(-2) = -30 (1b)

\frac{F(5)-F(3)}{5-3} = 20

F(5) - F(3) = 40 (2b)

We obtain the average value of f over the interval [-2, 5] by algebraic handling:

F(5) - F(3) +[F(3)-F(-2)] = 40 + (-30)

F(5) - F(-2) = 10

\frac{F(5)-F(-2)}{5-(-2)} = \frac{10}{5-(-2)}

\bar f = \frac{10}{7}

The average value of f over the interval [-2,5] is \frac{10}{7}.

4 0
2 years ago
Which choice number is the answer?
Luden [163]
The answer will be (2) 0 and 9
X^2(x-9)
X=0, and 9
3 0
3 years ago
Other questions:
  • Solve 15 + a = 31 for a
    11·2 answers
  • You have $96 I. A savings account and you deposit an equal amount into your account each week. After 7 weeks the account holds $
    5·1 answer
  • A garden hose emits 9 quarts of water in 6 seconds.How long will it take the hose to emit 12 quarts?
    8·2 answers
  • 9. Which equation can be used to determine A,<br> the area of the unshaded part of the figure?
    15·1 answer
  • Please help !!!!!!!!
    15·1 answer
  • A right triangle is shown. the base has a side length, b, of 30cm. the height, h, is 10cm. what is the length, in centimeters, o
    12·1 answer
  • Multiplying a fraction by a whole number 4/12,4/12,4/12,4/12,4/12
    15·1 answer
  • 9)
    6·2 answers
  • Determine if each set of ordered pairs represents a function.
    6·2 answers
  • 6,336 ft. = in league
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!